Bivariate generalization of the kummer-beta distribution
ABSTRACT: In this article, we study several properties such as marginal and conditional distributions, joint moments, and mixture representation of the bivariate generalization of the Kummer-Beta distribution. To show the behavior of the density function, we give some graphs of the density for diffe...
- Autores:
-
Bran Cardona, Paula Andrea
Orozco Castañeda, Johanna Marcela
Krishna Nagar, Daya
- Tipo de recurso:
- Article of investigation
- Fecha de publicación:
- 2011
- Institución:
- Universidad de Antioquia
- Repositorio:
- Repositorio UdeA
- Idioma:
- eng
- OAI Identifier:
- oai:bibliotecadigital.udea.edu.co:10495/29346
- Acceso en línea:
- http://hdl.handle.net/10495/29346
https://revistas.unal.edu.co/index.php/estad/article/view/29965
- Palabra clave:
- Funciones hipergeométricas
Hypergeometric functions
Distribución hipergeométrica
Hypergeometric distribution
Distribución (teoría de probabilidades)
Distribution (probability theory)
- Rights
- openAccess
- License
- http://creativecommons.org/licenses/by/2.5/co/
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| dc.title.spa.fl_str_mv |
Bivariate generalization of the kummer-beta distribution |
| dc.title.alternative.spa.fl_str_mv |
Generalización bivariada de la distribución kummer-beta |
| title |
Bivariate generalization of the kummer-beta distribution |
| spellingShingle |
Bivariate generalization of the kummer-beta distribution Funciones hipergeométricas Hypergeometric functions Distribución hipergeométrica Hypergeometric distribution Distribución (teoría de probabilidades) Distribution (probability theory) |
| title_short |
Bivariate generalization of the kummer-beta distribution |
| title_full |
Bivariate generalization of the kummer-beta distribution |
| title_fullStr |
Bivariate generalization of the kummer-beta distribution |
| title_full_unstemmed |
Bivariate generalization of the kummer-beta distribution |
| title_sort |
Bivariate generalization of the kummer-beta distribution |
| dc.creator.fl_str_mv |
Bran Cardona, Paula Andrea Orozco Castañeda, Johanna Marcela Krishna Nagar, Daya |
| dc.contributor.author.none.fl_str_mv |
Bran Cardona, Paula Andrea Orozco Castañeda, Johanna Marcela Krishna Nagar, Daya |
| dc.subject.lemb.none.fl_str_mv |
Funciones hipergeométricas Hypergeometric functions Distribución hipergeométrica Hypergeometric distribution Distribución (teoría de probabilidades) Distribution (probability theory) |
| topic |
Funciones hipergeométricas Hypergeometric functions Distribución hipergeométrica Hypergeometric distribution Distribución (teoría de probabilidades) Distribution (probability theory) |
| description |
ABSTRACT: In this article, we study several properties such as marginal and conditional distributions, joint moments, and mixture representation of the bivariate generalization of the Kummer-Beta distribution. To show the behavior of the density function, we give some graphs of the density for different values of the parameters. Finally, we derive the exact and approximate distribution of the product of two random variables which are distributed jointly as bivariate Kummer-Beta. The exact distribution of the product is derived as an infinite series involving Gauss hypergeometric function, whereas the beta distribution has been used as an approximate distribution. Further, to show the closeness of the approximation, we have compared the exact distribution and the approximate distribution by using several graphs. An application of the results derived in this article is provided to visibility data from Colombia |
| publishDate |
2011 |
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2011 |
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2022-06-21T21:21:47Z |
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2022-06-21T21:21:47Z |
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Artículo de investigación |
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0120-1751 |
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http://hdl.handle.net/10495/29346 |
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2389-8976 |
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https://revistas.unal.edu.co/index.php/estad/article/view/29965 |
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0120-1751 2389-8976 |
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http://hdl.handle.net/10495/29346 https://revistas.unal.edu.co/index.php/estad/article/view/29965 |
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eng |
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eng |
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Rev. Colomb. Estad. |
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Universidad Nacional de Colombia, Facultad de Ciencias, Departamento de Estadística |
| dc.publisher.group.spa.fl_str_mv |
Análisis Multivariado |
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Bogotá, Colombia |
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Universidad de Antioquia |
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Bran Cardona, Paula AndreaOrozco Castañeda, Johanna MarcelaKrishna Nagar, Daya2022-06-21T21:21:47Z2022-06-21T21:21:47Z20110120-1751http://hdl.handle.net/10495/293462389-8976https://revistas.unal.edu.co/index.php/estad/article/view/29965ABSTRACT: In this article, we study several properties such as marginal and conditional distributions, joint moments, and mixture representation of the bivariate generalization of the Kummer-Beta distribution. To show the behavior of the density function, we give some graphs of the density for different values of the parameters. Finally, we derive the exact and approximate distribution of the product of two random variables which are distributed jointly as bivariate Kummer-Beta. The exact distribution of the product is derived as an infinite series involving Gauss hypergeometric function, whereas the beta distribution has been used as an approximate distribution. Further, to show the closeness of the approximation, we have compared the exact distribution and the approximate distribution by using several graphs. An application of the results derived in this article is provided to visibility data from ColombiaRESUMEN: En este artículo, definimos la función de densidad de la generalización bivariada de la distribución Kummer-Beta. Estudiamos algunas de sus propiedades y casos particulares, así como las distribuciones marginales y condicionales. Para ilustrar el comportamiento de la función de densidad, mostramos algunos gráficos para diferentes valores de los parámetros. Finalmente, encontramos la distribución del producto de dos variables cuya distribución conjunta es Kummer-Beta bivariada y utilizamos la distribución beta como una aproximación. Además, con el fin de comparar la distribución exacta y la aproximada de este producto, mostramos algunos gráficos. Se presenta una aplicación a datos climáticos sobre niebla y neblina de Colombia.COL000053216application/pdfengUniversidad Nacional de Colombia, Facultad de Ciencias, Departamento de EstadísticaAnálisis MultivariadoBogotá, Colombiainfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_2df8fbb1https://purl.org/redcol/resource_type/ARTArtículo de investigaciónhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by/2.5/co/http://purl.org/coar/access_right/c_abf2https://creativecommons.org/licenses/by/4.0/Bivariate generalization of the kummer-beta distributionGeneralización bivariada de la distribución kummer-betaFunciones hipergeométricasHypergeometric functionsDistribución hipergeométricaHypergeometric distributionDistribución (teoría de probabilidades)Distribution (probability theory)Rev. Colomb. Estad.Revista Colombiana de Estadística497512343CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8927https://bibliotecadigital.udea.edu.co/bitstream/10495/29346/2/license_rdf1646d1f6b96dbbbc38035efc9239ac9cMD52LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://bibliotecadigital.udea.edu.co/bitstream/10495/29346/3/license.txt8a4605be74aa9ea9d79846c1fba20a33MD53ORIGINALOrozcoJohanna_2011_BivariateGeneralizationKummerBeta.pdfOrozcoJohanna_2011_BivariateGeneralizationKummerBeta.pdfArtículo de investigaciónapplication/pdf1247166https://bibliotecadigital.udea.edu.co/bitstream/10495/29346/1/OrozcoJohanna_2011_BivariateGeneralizationKummerBeta.pdf2d86ff7e4b2fbe3e1678c8ec9b7d8546MD5110495/29346oai:bibliotecadigital.udea.edu.co:10495/293462022-06-21 16:21:47.431Repositorio Institucional Universidad de Antioquiaandres.perez@udea.edu.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 |